Is there research that employs realistic models of neurons?
It looks like you really have two questions here. I'll try to answer the first one, and you should think about making a separate question for the second.

There is research into using simulated models of biologically realistic neurons. While there are large projects like the Human Brain Project aimed at simulating human brains, there is also a lot of lower-level AI research. SPAWN is an interesting system that got a lot of press a few years ago, and has continued to be developed since then. It uses realistic neurons to simulate several brain-regions at once, creating a surprisingly general AI system that could perform many types of motor and vision tasks using the same basic design.